1. **Stating the problem:** Solve the equation $8x + 75 = 180$ for $x$. 2. **Isolate the variable term:** Subtract 75 from both sides: $$8x = 180 - 75$$ $$8x = 105$$ 3. **Solve for $x$:** Divide both sides by 8: $$x = \frac{105}{8} = 13.125$$ 4. **Interpreting the triangle angles:** Given angles $75^\circ$, $x^\circ$, and $2x^\circ$, the sum of angles in a triangle is $180^\circ$: $$75 + x + 2x = 180$$ $$3x = 180 - 75 = 105$$ $$x = \frac{105}{3} = 35^\circ$$ 5. **Solving for $t$ in the equation $x^2 - t = 0$:** - For $x=4$: $$4^2 - t = 0$$ $$16 - t = 0$$ $$t = 16$$ - For $x=-4$: $$(-4)^2 - t = 0$$ $$16 - t = 0$$ $$t = 16$$ **Final answers:** - $x = 13.125$ from the linear equation. - $x = 35^\circ$ as the angle in the triangle. - $t = 16$ from the quadratic equation.